Minimum function

GAMS
1

Hello all,


How can I fix a variable to be the minimum of two other variables in an equation?

ie,

x(i,j)=min(y(i),y(j))


is there anyway that I can do it in an equation?


Thanks

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2

I have an answer but not necessarily correct.
If we assume the minimum of y(i) and y(j) is x(i,j) then:

x(i,j) wrote:

Hello all,


How can I fix a variable to be the minimum of two other variables in an equation?

ie,

x(i,j)=min(y(i),y(j))


is there anyway that I can do it in an equation?


Thanks

–
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3

Hi Fateme,

I am not sure whether it can be accomplished in a single equation, but I think it can be realized by some inequalities.
It is easier if the x(i,j) is the target:

x(i,j) <= y(i)
x(i,j) <= y(j)

then maximize variable x(i,j).
If x(i,j) is not the target, the formulation would be a little bit complicated:

x(i,j)-y(i)<=M*(1-z(i,j))
y(i)-x(i,j)<=M*(1-z(i,j))
x(i,j)-y(j)<=Mz(i,j)
y(j)-x(i,j)<=Mz(i,j)
y(i)-y(j)<=M*(1-z(i,j))
y(j)-y(i)<=M*z(i,j)

where z(i,j) is binary variable and M is a sufficiently large parameter.

Regards,
Dylan

在 2013年12月6日星期五UTC+8上午1时49分00秒，Fateme Fotuhi写道：

Hello all,


How can I fix a variable to be the minimum of two other variables in an equation?

ie,

x(i,j)=min(y(i),y(j))


is there anyway that I can do it in an equation?


Thanks

–
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4

Hi Fateme

Some solvers allow you to use the min-function (Path/Pathnlp for example).

Cheers

Renger




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From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of Fateme Fotuhi
Sent: Thursday, December 5, 2013 6:49 PM
To: gamsworld@googlegroups.com
Subject: Minimum function



Hello all,





How can I fix a variable to be the minimum of two other variables in an equation?



ie,



x(i,j)=min(y(i),y(j))





is there anyway that I can do it in an equation?





Thanks

–
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